Measurement of the Charge Form Factor of the
Neutron GnE from de e n p at
Q2 05 and 10 GeV c2
¼
N. Savvinov, for the E93-026 JLab collaboration
Department of Physics, University of Maryland, College Park, USA
Abstract. We determined the electric form factor of the neutron G nE via the reaction de e¼ n p using a longitudinally polarized electron beam and a frozen polarized 15 ND3 target at Jefferson Lab.
The knocked out neutrons were detected in a segmented plastic scintillator in coincidence with
the quasi-elastically scattered electrons which were tracked in Hall C’s High Momentum Spectrometer. To extract G nE , we compared the experimental beam–target asymmetry with theoretical
calculations based on different G nE models. We report the preliminary results of the fall 2001 run at
Q2 05 and 10 GeV c 2 .
INTRODUCTION
In a non-relativistic picture, the charge form-factor of the neutron GnE is related to the
charge distribution in the neutron and thus is important for our understanding of electromagnetic structure of nucleons. Despite a great effort focused on its determination,
GnE remains poorly known. Two major difficulties faced by experimenters in their studies of GnE are its small magnitude and the lack of a free neutron target. Unpolarized
cross-section measurements, from which GnE was extracted until 1990’s, were incapable
of overcoming these difficulties and yielded inconsistent or model-dependent results.
Recent technological advances in high duty factor accelerators, polarized sources,
polarized targets and recoil polarimetry made possible double polarization methods of
determining GnE . These methods use asymmetries rather than cross-sections and thus
reduce sensitivity to systematic errors.
In the experiment described here a longitudinally polarized electron beam was scattered off a polarized deuterated ammonia target. The polarized electron-neutron scattering cross section consists of helicity-independent and helicity-flip terms. The helicity
induced asymmetry, given by the ratio of these two terms, depends on G nE . For a general
orientation of the target polarization this dependence is complex. In order to minimize
the influence of the magnetic form factor GnM and maximize the sensitivity to G nE , the direction of the target polarization was chosen to be perpendicular to the three-momentum
transfer q and to lie in the scattering plane. For this case the expression for the electronneutron asymmetry Aen simplifies to the following:
2 τ 1 τ GnM GnE
Aen n 2
GE τ 1 21 τ tan2 θe2GnM 2
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
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Q
where τ 4M
2 , M is the neutron mass, and θ e is the electron scattering angle.
Since neutrons in deuterium are not free, the measured electron-deuteron asymmetry AVed differs from Aen due to reaction mechanisms such as final state interactions and
meson exchange currents. These reaction mechanisms were taken into account in theoretical calculations used for extraction of GnE [1].
2
EXPERIMENTAL SETUP
The experiment E93-026 was conducted in Hall C of Thomas Jefferson Accelerator
Facility (Jefferson Lab) in 1998 and 2001. The measurements were taken at two points,
Q2 05 and 10 GeV c2 .
The beam polarization was measured using a Moeller polarimeter. The average beam
polarization during the experiment was 75%. The beam current was limited to 100 nA
to avoid excessive thermal and radiation damage to the target polarization. A system of
raster magnets was used to distribute these stresses uniformly over the full target cell.
The readings of the raster magnets were also used by the reconstruction algorithm to
determine the horizontal and vertical position of the interaction point.
The solid polarized target [2] was developed by University of Virginia and was successfully used in two experiments prior to being used in E93-026. The basic components
of the polarized target include a superconducting magnet operated at 5 Tesla, a 4 He
evaporation refrigerator, a pumping system, a high power microwave tube operating at
frequencies around 140 GHz and an NMR system for measuring the target polarization.
The target material was polarized using the principle of dynamic nuclear polarization.
Target polarization was determined by measuring the impedance change of the series
resonant LCR circuit due to the nuclear magnetic moment. The conversion constants between the area of the NMR signal and the target polarization were obtained by a series
of thermal equilibrium measurements. The target polarization typically varied between
15% and 35% and averaged to 22%.
After interaction in the target material, the scattered electrons were detected in the
High Momentum Spectrometer of Hall C. Recoil nucleons were detected in the neutron
detector which consisted of six planes of thick scintillators and two planes of thin
scintillators. The latter were used for particle identification. The detector was set along
the direction of the three-momentum transfer and was enclosed in a concrete hut open
towards the target. The neutron vertical position was determined by the segmentation of
the detector while the horizontal position was determined from the time difference of
the phototubes.
ANALYSIS AND RESULTS
The electrons in the HMS were reconstructed using the standard HMS reconstruction
code extended for the effects of beam raster and target magnetic field. On the neutron
detector side a custom tracking algorithm was developed for proper particle identification. Neutrons were defined as events with no hits in the paddles along the track to
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E93-026 Preliminary
E93-026 (98)
3→ →
He(e,e'n) Mainz
2→ →
H(e,e'n) NIKHEF
2 → →
H(e,e'n) Mainz
GEn
0.1
0.05
Galster
0
0
0.5
1
2
1.5
2
Q (GeV/c)
FIGURE 1. Double polarization world data on G nE . Filled circle: preliminary E93-026 2001 data (error
bars only), filled square: final E93-026 result for 1998 data [3], open triangles: polarized helium data [4],
open squares: recoil polarimetry data [5, 6], open circle: NIKHEF polarized deuterium data [7].
the target, within a narrow time interval and within a 100 MeV range of invariant mass
around the nucleon mass. A number of other cuts was applied to optimize the dilution
factor and limit the recoil momentum to values where nuclear corrections are small.
After event reconstruction and event selection, charge and dead-time normalized
yields were produced for each beam helicity state, N and N . From these yields the
raw asymmetry ε was calculated:
ε
N N
N N
PBPT f AVed In order to obtain AVed from the raw asymmetry ε , one needs the knowledge of dilution
factor f (due to scattering from unpolarized materials) in addition to beam and target
polarizations PB and Pt . Dilution factor was calculated using montecarlo simulations.
Finally, AVed was corrected for accidental background and radiative effects.
The GnE was extracted by comparing the corrected experimental asymmetry to the
theoretical asymmetry averaged over the experimental acceptance under different assumptions about the size of the G nE . Preliminary results are consistent with the Galster
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parametrization. The systematic error is expected to be dominated by uncertainty in target polarization (3-5%) and dilution factor ( 3%).
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